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3.8 LIQUEFYING GASES USING AN ISENTHALPIC EXPANSION 63

Example Problem 3.11 shows that for an ideal gas, m J-T is zero. It can be shown 700
that for a van der Waals gas in the limit of zero pressure
600
1 2a N
m J-T = a - bb (3.54) 2
C P,m RT 500
Temperature/K 400

Liquefying Gases Using an Isenthalpic 300
3.8 Expansion
200 H 2
For real gases, the Joule-Thomson coefficient m J-T can take on either negative or
positive values in different regions of P–T space. If m J-T is positive, a decrease in 100
pressure leads to a cooling of the gas; if it is negative, the expansion of the gas
leads to a heating. Figure 3.6 shows the variation of m J-T with T and P for N 2 and
H 2 . All along the solid curve, m J-T = 0 . To the left of each curve, m J-T is positive, 100 200 300 400 500
and to the right, it is negative. The temperature for which m J-T = 0 is referred to Pressure/atm
as the inversion temperature. If the expansion conditions are kept in the region in FIGURE 3.6
which m J-T is positive, ¢T can be made sufficiently large as ¢P decreases in the All along the curves in the figure,
expansion to liquefy the gas. Note that Equation (3.54) predicts that the inversion m J-T = 0 , and m J-T is positive to the left
temperature for a van der Waals gas is independent of P, which is not in agreement of the curves and negative to the right.
with experiment. To experience cooling upon expansion at
The results in Figure 3.6 are in accord with the observation that a high-pressure 100. atm, T must lie between 50. K and
. The corresponding temper-
(100 6 P 6 500 atm) expansion of N 2 at 300 K leads to cooling and that similar con- 150. K for H 2
ditions for H 2 lead to heating. To cool H 2 in an expansion, it must first be precooled atures for N 2 are 100. K and 650. K.
below 200 K, and the pressure must be less than 160 atm. He and H 2 are heated in an
isenthalpic expansion at 300 K for P 6 200 atm .
The Joule-Thomson effect can be used to liquefy gases such as N 2 , as shown in
Figure 3.7. The gas at atmospheric pressure is first compressed to a value of 50 atm to
200 atm, which leads to a substantial increase in its temperature. It is cooled and subse-
quently passed through a heat exchanger in which the gas temperature decreases to a
'
value within 50 K of the boiling point. At the exit of the heat exchanger, the gas
expands through a nozzle to a final pressure of 1 atm in an isenthalpic expansion. The
cooling that occurs because m J-T 7 0 results in liquefaction. The gas that boils away
passes back through the heat exchanger in the opposite direction than the gas to be liq-
uefied is passing. The two gas streams are separated, but in good thermal contact. In
this process, the gas to be liquefied is effectively precooled, enabling a single-stage
expansion to achieve liquefaction.

Cooler

FIGURE 3.7
Schematic depiction of the liquefaction of
a gas using an isenthalpic Joule-Thomson
expansion. Heat is extracted from the gas
exiting from the compressor. It is further
Gas feed cooled in the countercurrent heat
Compressor exchanger before expanding through a
nozzle. Because its temperature is suffi-
ciently low at the exit to the countercur-
Liquid out rent heat exchanger, liquefaction occurs.